Indifference pricing [electronic resource] : theory and applications / edited by René Carmona.

ISBN:

9781400833115

Title:

Author:

Carmona, R. (René)

Publication Information:

Physical Description:

1 online resource (xi, 414 pages) : illustrations.

Series:

Princeton series in financial engineering

Contents:

Cover; Title; Copyright; Contents; Preface; PART 1. FOUNDATIONS; PART 2. DIFFUSION MODELS; PART 3. APPLICATIONS; PART 4. COMPLEMENTS; Bibliography; List of Contributors; Notation Index; Author Index; Subject Index.

Local Note:

eBooks on EBSCOhost

Subject Term:

Nonlinear pricing -- Mathematical models.

Prices -- Mathematical models.

Added Author:

Carmona, R. (René)

Format:

Electronic Resources

Electronic Access:

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Publication Date:

2009

Publication Information:

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Summary

This is the first book about the emerging field of utility indifference pricing for valuing derivatives in incomplete markets. René Carmona brings together a who's who of leading experts in the field to provide the definitive introduction for students, scholars, and researchers. Until recently, financial mathematicians and engineers developed pricing and hedging procedures that assumed complete markets. But markets are generally incomplete, and it may be impossible to hedge against all sources of randomness. Indifference Pricing offers cutting-edge procedures developed under more realistic market assumptions.

The book begins by introducing the concept of indifference pricing in the simplest possible models of discrete time and finite state spaces where duality theory can be exploited readily. It moves into a more technical discussion of utility indifference pricing for diffusion models, and then addresses problems of optimal design of derivatives by extending the indifference pricing paradigm beyond the realm of utility functions into the realm of dynamic risk measures. Focus then turns to the applications, including portfolio optimization, the pricing of defaultable securities, and weather and commodity derivatives. The book features original mathematical results and an extensive bibliography and indexes.

In addition to the editor, the contributors are Pauline Barrieu, Tomasz R. Bielecki, Nicole El Karoui, Robert J. Elliott, Said Hamadène, Vicky Henderson, David Hobson, Aytac Ilhan, Monique Jeanblanc, Mattias Jonsson, Anis Matoussi, Marek Musiela, Ronnie Sircar, John van der Hoek, and Thaleia Zariphopoulou.

The first book on utility indifference pricing
Explains the fundamentals of indifference pricing, from simple models to the most technical ones
Goes beyond utility functions to analyze optimal risk transfer and the theory of dynamic risk measures
Covers non-Markovian and partially observed models and applications to portfolio optimization, defaultable securities, static and quadratic hedging, weather derivatives, and commodities
Includes extensive bibliography and indexes
Provides essential reading for PhD students, researchers, and professionals

Author Notes

René Carmona is the Paul M. Wythes '55 Professor of Engineering and Finance in the Department of Operations Research and Financial Engineering at Princeton University. His books include Interest Rate Models and Statistical Analysis of Financial Data in S-Plus .

Marek Musiela and Thaleia ZariphopoulouVicky Henderson and David HobsonPauline Barrieu and Nicole El KarouiRené CarmonaAytac Ilhan and Mattias Jonsson and Ronnie SircarTomasz R. Bielecki and Monique JeanblancRené CarmonaNicole El Karoui and Said Hamadène and Anis MatoussiRobert J. Elliott and John van der Hoek

Preface	p. ix
Part 1 Foundations	p. 1
Chapter 1 The Single Period Binomial Model	p. 3
1.1 Introduction	p. 3
1.2 The Incomplete Model	p. 5
Chapter 2 Utility Indifference Pricing: An Overview	p. 44
2.1 Introduction	p. 44
2.2 Utility Functions	p. 45
2.3 Utility Indifference Prices: Definitions	p. 48
2.4 Discrete Time Approach to Utility Indifference Pricing	p. 51
2.5 Utility Indifference Pricing in Continuous Time	p. 52
2.6 Applications, Extensions, and a Literature Review	p. 65
2.7 Related Approaches	p. 68
2.8 Conclusion	p. 72
Part 2 Diffusion Models	p. 75
Chapter 3 Pricing, Hedging, and Designing Derivatives with Risk Measures	p. 77
3.1 Indifference Pricing, Capital Requirement, and Convex Risk Measures	p. 78
3.2 Dilatation of Convex Risk Measures, Subdifferential and Conservative Price	p. 93
3.3 Inf-Convolution	p. 98
3.4 Optimal Derivative Design	p. 105
3.5 Recalls on Backward Stochastic Differential Equations	p. 118
3.6 Axiomatic Approach and g-Conditional Risk Measures	p. 120
3.7 Dual Representation of g-Conditional Risk Measures	p. 128
3.8 Inf-Convolution of g-Conditional Risk Measures	p. 136
3.9 Appendix: Some Results in Convex Analysis	p. 141
Chapter 4 From Markovian to Partially Observable Models	p. 147
4.1 A First Diffusion Model	p. 147
4.2 Static Hedging with Liquid Options	p. 154
4.3 Non-Markovian Models with Full Observation	p. 159
4.4 Optimal Hedging in Partially Observed Markets	p. 169
4.5 The Conditionally Gaussian Case	p. 174
Part 3 Applications	p. 181
Chapter 5 Portfolio Optimization	p. 183
5.1 Introduction	p. 183
5.2 Indifference Pricing and the Dual Formulation	p. 186
5.3 Utility Indifference Pricing	p. 190
5.4 Stochastic Volatility Models	p. 197
Chapter 6 Indifference Pricing of Defaultable Claims	p. 211
6.1 Preliminaries	p. 211
6.2 Indifference Prices Relative to the Reference Filtration	p. 216
6.3 Optimization Problems and BSDEs	p. 222
6.4 Quadratic Hedging	p. 230
Chapter 7 Applications to Weather Derivatives and Energy Contracts	p. 241
7.1 Application I: Temperature Options	p. 241
7.2 Application II: Rainfall Options	p. 249
7.3 Application III: Commodity Derivatives	p. 256
Part 4 Complements	p. 265
Chapter 8 BSDEs and Applications	p. 267
8.1 General Results on Backward Stochastic Differential Equations	p. 269
8.2 Applications to Optimization Problems	p. 279
8.3 Markovian BSDEs	p. 285
8.4 BSDEs with Quadratic Growth with Respect to Z	p. 296
8.5 Reflected Backward Stochastic Differential Equations	p. 303
Chapter 9 Duality Methods	p. 321
9.1 Introduction	p. 321
9.2 Model	p. 322
9.3 Utility Functions	p. 325
9.4 Pricing Claims	p. 326
9.5 The Dual Cost Function	p. 333
9.6 The Minimum of VG(y) and V0(y)	p. 341
9.7 The Calculation of V0(x)	p. 346
9.8 The Indifference Asking Price for Claims	p. 348
9.9 The Indifference Bid Price	p. 355
9.10 Examples	p. 356
9.11 Properties of ?	p. 361
9.12 Numerical Methods	p. 364
9.13 Approximate Formulas	p. 374
9.14 An Alternative Representation for VG(x)	p. 381
Bibliography	p. 387
List of Contributors	p. 405
Notation Index	p. 409
Author Index	p. 410
Subject Index	p. 413

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Table of Contents